Answer the query please, QUERY: Suppose capital were not fixed in this problem. How should capital and labor be allocated between the two farms?

EXAMPLE 13.6 Gains from Efficiently Allocating Labor To examine the quantitative gains in output from allocating resources efficiently, suppose two rice farms have production functions of the simple form 1 = kl/413/4 (13.58) but that one rice farm is more mechanized than the other. If capital for the first farm is given by k, = 16 and for the second farm by &, = 625, then (13.59) 13/4 12 = 5/2 If the total labor supply is 100, an equal allocation of labor to these two farms will provide total rice output of 2 = 41 + 42 = 2(50)3/* + 5(50)3/4 = 131.6. (13.60) The efficient allocation is found by equalizing the marginal productivityes: -1/4 _ 092 15 ,-1/4 (13.61) ye al, Hence, for efficiency, labor should be allocated such that 4 = 1 = 0.025612- (13.62) Given the greater capitalization of farm 2, practically all of the available labor should be devoted to it. With 100 units of labor, 97.4 units should be allocated to farm 2 with only 2.6 units to farm 1. In this case total output will be 2 =41 + 42 = 2(2.6)3/# +5(97.4)3/# = 159.1. (13.63) This represents a gain of more than 20 percent over the rice output obtained under the equal allocation. QUERY: Suppose capital were not fixed in this problem. How should capital and labor be allocated between the two farms